Answer by Narasimham for Light rays bouncing in twisted tubes
Just a guess .. tend to think that all (in laser-like beam) rays entering the torus: $$ (c + a \cos \phi ) \cos\theta,(c + a \cos \phi ) \sin \theta,a \sin \phi ) $$remain inside of the twisted torus...
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Answer by Dmitri Panov for Light rays bouncing in twisted tubes
I would like to add one more piece of information and some pictures concerning the snake like tube. All this was communicated to me by Peter Panov.To analyze the movement of a ray in the tube we will...
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Answer by Joseph O'Rourke for Light rays bouncing in twisted tubes
Here is my interpretation of Anton's idea to capture the ray.I found it almost impossible to illustrate; I could only show three sections of thetube, separated by two rotations, the first...
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Answer by Joseph O'Rourke for Light rays bouncing in twisted tubes
Here is the phase portrait of $(\theta, x \; \mathrm{mod} \; 2)$ for the rays that Dimitri suggestedin his response to Q2(if I have interpreted his suggestion correctly), using the samedata as...
View ArticleAnswer by Dmitri Panov for Light rays bouncing in twisted tubes
Edited 1. Some suggestions are added at the end concerning Q2.Edited 2. An "explanation" of spikes at $17^0$ is added at the very end... Q1 I think that the answer to Q1 is positive provided the...
View ArticleAnswer by Anton Petrunin for Light rays bouncing in twisted tubes
Q1. No.The projection of the ray to the curve $c(t)$ has to be monotonic.In particular, no ray can come back, but some ray might stay in the tube forever.Construction. The curve and ray will be...
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Light rays bouncing in twisted tubes
Imagine a smooth curve $c$ sweeping out a unit-radius disk that isorthogonal to the curve at every point.Call the result a tube.I want to restrict the radius of curvature of $c$ to be at most 1.I am...
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